Abstract: We show that a simple transformation between the regular lattices (the square, the triangular, and the honeycomb) belonging to the same dimensionality can explain in a natural way the universality of the critical exponents found in phase transitions and critical phenomena. It suffices that the Hamiltonian and the lattice present similar writing forms. In addition, it appears that if a property can be calculated for a given lattice then it can be extrapolated simply to any other lattice belonging to the same dimensionality. In this study, we have restricted ourselves on the spectral power amplification (SPA), we note that the SPA does not have an effect on the critical exponents but does have an effect by the criticality temperature of the lattice; the generalisation to other lattice could be shown according to the containment principle.
Abstract: This paper presents an approach to reduce some of its current flaws in the requirements phase inside the software development process. It takes the software requirements of an application, makes a conceptual modeling about it and formalizes it within JSON documents. This formal model is lodged in a NoSQL database which is document-oriented, that is, MongoDB, because of its advantages in flexibility and efficiency. In addition, this paper underlines the contributions of the detailed approach and shows some applications and benefits for the future work in the field of automatic code generation using model-driven engineering tools.
Abstract: The Ising ferromagnet, consisting of magnetic spins, is
the simplest system showing phase transitions and critical phenomena
at finite temperatures. The Ising ferromagnet has played a central role
in our understanding of phase transitions and critical phenomena.
Also, the Ising ferromagnet explains the gas-liquid phase transitions
accurately. In particular, the Ising ferromagnet in a nonzero magnetic
field has been one of the most intriguing and outstanding unsolved
problems. We study analytically the partition function zeros in the
complex magnetic-field plane and the Yang-Lee edge singularity of
the infinite-range Ising ferromagnet in an external magnetic field.
In addition, we compare the Yang-Lee edge singularity of the
infinite-range Ising ferromagnet with that of the square-lattice Ising
ferromagnet in an external magnetic field.
Abstract: We constructed a method of phase unwrapping for a typical wave-front by utilizing the maximizer of the posterior marginal (MPM) estimate corresponding to equilibrium statistical mechanics of the three-state Ising model on a square lattice on the basis of an analogy between statistical mechanics and Bayesian inference. We investigated the static properties of an MPM estimate from a phase diagram using Monte Carlo simulation for a typical wave-front with synthetic aperture radar (SAR) interferometry. The simulations clarified that the surface-consistency conditions were useful for extending the phase where the MPM estimate was successful in phase unwrapping with a high degree of accuracy and that introducing prior information into the MPM estimate also made it possible to extend the phase under the constraint of the surface-consistency conditions with a high degree of accuracy. We also found that the MPM estimate could be used to reconstruct the original wave-fronts more smoothly, if we appropriately tuned hyper-parameters corresponding to temperature to utilize fluctuations around the MAP solution. Also, from the viewpoint of statistical mechanics of the Q-Ising model, we found that the MPM estimate was regarded as a method for searching the ground state by utilizing thermal fluctuations under the constraint of the surface-consistency condition.
Abstract: In this paper the design of maximally flat linear phase
finite impulse response (FIR) filters is considered. The problem is
handled with totally two different approaches. The first one is
completely deterministic numerical approach where the problem is
formulated as a Linear Complementarity Problem (LCP). The other
one is based on a combination of Markov Random Fields (MRF's)
approach with messy genetic algorithm (MGA). Markov Random
Fields (MRFs) are a class of probabilistic models that have been
applied for many years to the analysis of visual patterns or textures.
Our objective is to establish MRFs as an interesting approach to
modeling messy genetic algorithms. We establish a theoretical result
that every genetic algorithm problem can be characterized in terms of
a MRF model. This allows us to construct an explicit probabilistic
model of the MGA fitness function and introduce the Ising MGA.
Experimentations done with Ising MGA are less costly than those
done with standard MGA since much less computations are involved.
The least computations of all is for the LCP. Results of the LCP,
random search, random seeded search, MGA, and Ising MGA are
discussed.
Abstract: A zero-field ferromagnetic Ising model is utilized to
simulate the propagation of infection in a population that assumes a
square lattice structure. The rate of infection increases with
temperature. The disease spreads faster among individuals with low J
values. Such effect, however, diminishes at higher temperatures.
Abstract: The square-lattice Ising model is the simplest system
showing phase transitions (the transition between the paramagnetic
phase and the ferromagnetic phase and the transition between the
paramagnetic phase and the antiferromagnetic phase) and critical
phenomena at finite temperatures. The exact solution of the squarelattice
Ising model with free boundary conditions is not known for
systems of arbitrary size. For the first time, the exact solution of
the Ising model on the square lattice with free boundary
conditions is obtained after classifying all )
spin configurations with the microcanonical transfer matrix. Also, the
phase transitions and critical phenomena of the square-lattice Ising
model are discussed using the exact solution on the square
lattice with free boundary conditions.
Abstract: Weather systems use enormously complex
combinations of numerical tools for study and forecasting.
Unfortunately, due to phenomena in the world climate, such
as the greenhouse effect, classical models may become
insufficient mostly because they lack adaptation. Therefore,
the weather forecast problem is matched for heuristic
approaches, such as Evolutionary Algorithms.
Experimentation with heuristic methods like Particle Swarm
Optimization (PSO) algorithm can lead to the development of
new insights or promising models that can be fine tuned with
more focused techniques. This paper describes a PSO
approach for analysis and prediction of data and provides
experimental results of the aforementioned method on realworld
meteorological time series.